Palestinian militant group Hamas is on the verge of renewing its offer to end attacks in Israel as the efforts to renew the United States-sponsored peace process gain pace.

Sources say the group, which tried to blow up an Israeli bus in Gaza on Friday, is being forced into its decision by a combination of international and domestic pressure. It would be the ninth ceasefire to be offered or initiated by Hamas since the Oslo peace accords.

Despite a surge of bombings last weekend, the military leadership of Hamas is apparently tired of waging a seemingly endless war.

People living in Beit Hanoun in Gaza last week protested against Hamas's firing of rockets at Israel from their town. The Israeli army retaliated by levelling the town's citrus groves from where the rockets are fired.

Most importantly, Hamas faces having its funding from abroad cut. Syria and Iran are under immense pressure from the US to stop backing terrorist groups, while Saudi Arabia, believed to be Hamas's largest donor, is pressurising the group to give the new Palestinian Prime Minister, Abu Mazen, a chance.

Hamas's decision will be affected by the outcome of the Israeli government's debate on the 'road map', the latest Middle East peace initiative, which is expected to take place today or tomorrow. Ariel Sharon, the Israeli Prime Minister, agreed to accept the road map in return for US recognition of his reservations.

After a meeting with Abu Mazen and Mohammad Dahlan, the Palestinian Interior Minister, Ismail Hanieh, a spokesman for Hamas, said that the group would be willing to stop attacks within the borders of internationally recognised Israel if Israel stopped assassinating its leaders. However, he insisted that Hamas would continue to attack settlers and soldiers in the West Bank and Gaza.

A senior diplomat who maintains close contact with the Palestinian leadership said: 'Abu Mazen and his team are seriously convinced that Hamas has to be brought under control as a matter of Palestinian national interest apart from what the Israelis demand. Dahlan believes that he can get a ceasefire if the Israelis reciprocate. The Israeli acceptance of the road map would also be very helpful.'

Sceptics point out that Hamas killed nine people in a wave of suicide bombings last weekend in what appeared to be a determined effort to destroy the nascent peace process. However, Israeli intelligence agencies and Palestinian sources believe that Hamas is unable to plan attacks to order outside its Gaza stronghold.

In the last six months, during negotiations with Omar Suleiman, the head of Egyptian intelligence, Hamas has hinted that it might be willing to make a deal that would guarantee its political future and the lives of its leadership.

Qais Abu Leila, the leader of the Democratic Front for the Liberation of Palestine, a faction of the Palestine Liberation Organisation which launches sporadic attacks against Israeli military targets, survived an Israeli assassination attempt in 2001 and remains a wanted man.

He said: 'They may very well accept a conditional ceasefire. They are under enormous pressure from regional powers, including Saudi Arabia which provides most of Hamas's financial support. Syria is now neutral and there is evidence that even Iran is recalculating its position. They will have to balance that pressure with the pressure from the rank and file to continue the fight.

'I have absolutely no doubt that Hamas and probably Islamic Jihad will stop all military action if the Israelis withdraw from the West Bank and Gaza regardless of what they say at the moment.'

Abu Mazen has said that he wants to negotiate a ceasefire with Hamas, but in 1996 Yasser Arafat ordered the Palestinian Authority to launch a crackdown after 60 Israelis were killed in a series of bombings. Palestinian police arrested 1,000 activists and managed to reduce the number of Hamas attacks.

Israel has said it wants to see a rerun of 1996 with the disarming of Hamas, but the new Palestinian government does not believe it has the ability to carry out a hardline policy after the Israeli destruction of the Palestinian security infrastructure over the last 32 months. It also believes it will not have the political power to carry out such an operation until Israel begins easing its restrictions on Palestinian life.